Torben, I noticed something along those lines long ago: the first non-prime
Mersenne number is M11 which factors to 23 times 89. The very next non-prime
Mersenne number is M23, and M89 is also not prime. It occurred to me then
that possibly Mx is never prime if x is a factor of a Mersenne number, but
it was just an observation and I never got around to pursuing it. If so,
then it would (although only very slightly) reduce the number of candidates
to be tested. So I am just as curious as are you.
Jeroen, I am wondering about your phrase "if kv is not prime then 2^(kv)-1
isn't also" because kv is never prime, it has factors k and v (unless k=1,
of course), and 2^(kv)-1 always has factors 2^k-1 and 2^v-1. I don't know if
you meant something else or if I just misunderstood you. Sorry if that's the
case.
Regards,
Steve Harris
-----Original Message-----
From: Jeroen <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED] <[EMAIL PROTECTED]>
Date: Tuesday, March 19, 2002 8:12 PM
Subject: Re: Mersenne: Factors aren't just factors
>to find the value v where prime p is a factor of 2^v-1
>
>tempvalue = p
>count = 0
>while tempvalue != 0
>{
> if tempvalue is odd
> {
> shiftright tempvalue
> count++
> }
> else
> {
> tempvalue+=p
> }
>}
>
>if the count is a primenumber then p is thus a factor of a mersenne prime
>if the count is not a primenunber it isn't
>if p is a factor of 2^v-1 then it is also a factor of 2^(2v)-1
>or just 2^(kv)-1 for all value of k are integers above 0
>if kv is not prime them 2^(kv)-1 isn't also, so each prime can only be a
factor of one mersenne numer or 0 mersenne numbers
>the first question is now simple to solve, just find the 2^v-1 where Mx is
a factor of
>
>
>
>*********** REPLY SEPARATOR ***********
>
>On 20-3-02 at 0:21 Torben Schlüntz wrote:
>
>>Just of curiosity:
>>
>>Has it ever happened that a factor for Mx later has proved to be a
>>mersenne prime itself?
>>
>>Has the same factor been a factor for two different Mx and My?
>>
>>In my humble oppinion both questions answers No; but GIMPS could have
>>proved otherwise.
>>
>>Anyway, it must exist a great deal of low primes; which by now never can
>>become mersenne factors (by reason: 2kp+1). So with two types of primes,
>>those that are mersenne factors and those that never can be, do we have
>>any means of distinguish them?
>>
>>
>>Happy hunting
>>tsc
>>
>>Btw: (M29 mod 1 + M29 mod 2 +......+ M29 mod 32) = 233 which is 1.
>>factor of M29
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>
>
>
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